We show that the p-periodic logistic equation xn+1 = μn mod pxn(1 − xn) has cycles (periodic solutions) of minimal periods 1, p, 2p, 3p, .... Then we extend Singer’s theorem to periodic difference equations, and use it to show the p-periodic logistic equation has at most p stable cycles. Also, we present computational methods investigating the stable cycles in case p = 2 and 3.

For the equation with a distributed delay

Table of contents §9.0. Foreword. §9.1. My more general auxiliary functions in the case k = 1, 2, 3. §9.2. Some relations for the functions, considered in §9.1 in the case l = 0. §9.3. Passing to the system of difference equations for the functions, considered in §9.2. §9.4. Passing from (τ, μ), to (α, ν) in the case l = 0. §9.0. Foreword. Let |z| ≥ 1,−3π/2 < arg(z) ≤ π/2, log(z) = ln(|z|) + i ...

We start a general study of counting the number of occurrences of ordered patterns in words generated by morphisms. We consider certain patterns with gaps (classical patterns) and those with no gaps (consecutive patterns). Occurrences of the patterns are known, in the literature, as rises, descents, (non-)inversions, squares and p-repetitions. We give recurrence formulas in the general case, th...

Let {φn} be a sequence of rational functions with arbitrary complex poles, generated by a certain three-term recurrence relation. In this paper we show that under some mild conditions the rational functions φn form an orthonormal system with respect to a Hermitian positive-definite inner product.

Asymptotic stability for difference equations with decreasing arguments D. M. Chan , E. R. Chang , M. Dehghan , C. M. Kent , R. Mazrooei-Sebdani & H. Sedaghat To cite this article: D. M. Chan , E. R. Chang , M. Dehghan , C. M. Kent , R. Mazrooei-Sebdani & H. Sedaghat (2006) Asymptotic stability for difference equations with decreasing arguments, Journal of Difference Equations and Applications,...